DP
RIETI Discussion Paper Series 05-E-003
An Experimental Study of Leniency Programs
HAMAGUCHI Yasuyo
Kyoto Sangyo University
KAWAGOE Toshiji
RIETI
The Research Institute of Economy, Trade and Industry
http://www.rieti.go.jp/en/
RIETI Discussion Paper Series 05-E-003
An Experimental Study of Leniency Programs*
Yasuyo Hamaguchi,** Toshiji Kawagoe***
February 17, 2005
Abstract
Antitrust authorities of many countries have been trying to establish appropriate competition policies
based on economic analysis. Recently an anti-cartel policy called a “leniency program” has been
introduced in many countries as an effective policy to dissolve cartels. In this paper, we studied
several kinds of leniency programs through laboratory experiments. We experimentally controlled
for two factors: 1) cartel size: the number of cartel members in a group, small (two-person) or large
(seven-person), 2) schedule of reduced fine: the number of firms that are given reduced fines. The
experimental results showed that (1) an increase in the number of cartel members in a group
increased the number of cartels dissolved, (2) changing the coverage of reduced fine had no
significant effect both in two-player case and in seven-player case.
JEL Classification: C92, D43, K21, K42
Keywords: Leniency programs, Cartels, Collusion, Antitrust law, Experiment.
――――――――――――――――――――――――――――――――――――――――
＊This research was partially supported by the Ministry of Education, Science, Sports and Culture,
Grant-in-Aid for Young Scientists (B) and Research Institute of Economy, Trade and Industry. The
views expressed here are the personal views of the authors and do not reflect those of the institutions
to which they belong. The names of the authors are listed in alphabetical order.
＊＊Kyoto Sangyo University, Motoyama, Kamigamo, Kitaku, Kyoto, 603-8555, Japan; E-mail:
yhamagu@cc.kyoto-su.ac.jp
＊＊＊Future University - Hakodate, 116-2 Kameda Nakano-cho, Hakodate, Hokkaido, 041-8655,
Japan; E-mail: kawagoe@fun.ac.jp
Introduction
Cartels, collusions among competing firms, harm the social welfare of consumers by
restricting competition in markets. Such market restrictions include entry barriers,
market–dividing activities, price fixing, and volume controlling. The major role of
antitrust authorities (referred to hereafter as AA) is to restrain cartels. For example, the
Japan Fair Trade Commission (JFTC) made recommendations for 15 cases of price
fixing cartels and bid riggings in fiscal year 2003. Surcharge orders, which are legal
means to confiscate excessive profits created by cartels, were imposed on 468 firms and
the total amount of the surcharges amounted to 3.9 billion yen in fiscal year 2003.
Between fiscal years 1994 and 2003, JFTC took formal actions in 279 cases with a total
of 5798 firms. An international trend is one of strengthening fines and surcharges. For
example, JFTC submitted a major amendment to the Japanese Antimonopoly Act to the
Diet in 2004. The essential features of the revisions are that the basic surcharge rate
shall be increased from 6% to 10% and that a leniency program shall be introduced to
the surcharge system.1 Lowe describes EU’s future fine policy as follows:
The trend is clearly one of increasing fines, in order to achieve a genuine
dissuasive effect on firms. In 2001, the heaviest individual fine yet, 462 million
euros, was imposed against Hoffman-LaRoche in the Vitamins case. In 2002, the
second highest amount ever, 250 million euros, was imposed against Lafarge for
its participation in the Plasterboard cartel. Other significant fines were those
imposed on the BPB, also in Plasterboard, 139 million euros and 118 million
1
According to the JFTC’s annual reports. A formal action means recommendations or surcharge
payment orders without cease and desist orders preceding.
-1-
euros for Degussa for its role in the Methionine conspiracy.2
In order to raise the probability of detecting cartels, the leniency program has been
implemented in many countries, such as the EU, the US, Canada, Australia, Korea.
They have proven that the program is a very effective device to detect cartels. In the
EU, between 1996 and 2002, more than 80 firms cooperated with the EC Commission
under the leniency scheme and out of a total of 24 decisions imposing fines, firms in 17
cases cooperated with the Commission under the leniency scheme. 3 That is, the
number of cartels caught has increased dramatically under the leniency program.
A typical leniency program is carried out in the following way. If a member of a
cartel group resigns from the cartel and reports himself to the AA with sufficient
evidence of his cartel activity sooner than other cartel members, then his firm will be
given full leniency and will be exempted from paying a fine at all. Many countries’
AAs give “moderate leniency” (reduced fine) to firms that were not the first reporters
so that the authorities can get more hidden cartel information from those cartel
members, too. By introducing the program, cartel members might compete with each
other to reveal the evidence of their illegal activity to the AA to get the highest leniency.
If this is true, then the leniency program has the advantage of increasing the probability
of finding cartel activities without increasing enforcement costs.
Although there are some theoretical studies on various kinds of leniency programs
using repeated game theory (e.g. Motta and Polo (2003), Hinloopen (2002)), to our
knowledge, Apesteguia et al. (2003) is the only paper based on laboratory experiments.
Hinloopen (2002) theoretically analyzed European style leniency programs. In the
2
3
See Lowe (2003).
See Monti (2002).
-2-
European style leniency programs, a fine is considered to be proportional to gross
annual sales of a firm (maximum fine up to 10% of total sales). Hinloopen showed that
it is highly unlikely for a cartel member to report information to the AA unless the
probability of detection and/or a fine are unrealistically high. Brisset and Thomas
(2002) obtained very similar results in the simplified first price auction settings.
Compared with the European leniency program, Spagnolo (2000) proved that
courageous leniency programs, which give reward to self-reporting firms, may deter
collusion completely and costlessly.
Apesteguia et al. (2003) investigated leniency programs in a one-shot Bertrand
competition framework theoretically and experimentally. They compared several
variations of leniency programs including courageous leniency program proposed a la
Spagnolo, and found that the rate of cartel formation was the highest in the case that a
reward was provided for the action of reporting, which contradicts the theoretical
predictions.
In this paper, we also studied the enforcement of competition policy against
collusion under two kinds of leniency programs in laboratory settings. Since only
unilateral deviations from the equilibrium are to be considered according to the Nash
equilibrium concept, the equilibrium predictions in the two-person game models used
in previous studies can be applied to the case where the game consists of more than
two players, and the case where the coverage of reduced fine is limited only to the first
reporting firm. However, we are not sure whether these predictions are true in real
situations. If every firm involved in a cartel activity can give legally sufficient cartel
information to the AA, the cartel can be dissolved easily just by prosecuting one firm.
That might make each cartel member rely less on collusion as the number of cartel
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members increases. In addition, cartels might be dissolved much faster with the
leniency program than without it, since if a firm reports the cartel information to the
AA, they can avoid a considerable fine when the cartel is detected by the AA.
Furthermore, such a deviation from collusion could be accelerated if only the first
reporting firm can avoid the fine and others get a penalty.
To investigate these institutional design issues, we must consider what are the
crucial variables that the AA can manipulate to prevent firms from forming cartels.
The variables the AA can control but firms can not are the probability of investigation
and the level of the surcharge or fine. Those variables can influence the incentive of
firms for cartel formation greatly. If the probability of being caught and the fine are
very low (or high), firms believe that the expected profits that they could gain from the
cartel would be greater (or smaller) than the expected losses from being caught.
Based on the considerations above, we experimentally controlled the following two
factors to compare several institutional designs of leniency programs in a simplified
oligopoly market:
(1) Cartel group size: the number of cartel members in a group is either small (two
members) or large (seven members),
(2) The schedule of reduced fine: the number of firms that are given reduced fines is
either only the first reporter or all firms that report the cartel information.
The model in our experiments is as follows. First, the probability of being
investigated by the AA is common knowledge among firms. Each cartel member
colludes in an N-person prisoners’ dilemma game first, and then, they voluntarily and
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independently decide whether or not to report the cartel information to the AA. If at
least one player in a group reports the information, then their collusion in the prisoners’
dilemma is revealed to the AA with certainty, and all but the players who reported the
information suffer the full fine (F), and the players who reported the information suffer
only a reduced fine (R (< F)). Even if no one in a group reports the cartel information,
the collusion is detected by the AA with the probability (p), and every member of the
group suffers the full fine if the collusion is detected.
Although it is very important to investigate whether people would collude in the
beginning under the leniency programs, the issue we deal with here is limited only to
how the leniency program works under the situation where firms already collude with
each other.4 To make our subjects understand that sustaining a cartel is the most
profitable for them, they experienced the mutually cooperative outcome of the
prisoners’ dilemma game for a sufficient number of periods. Then, we ran two
treatments with leniency programs.
The experimental results showed that (1) the large size cartel is more easily
dissolved than the small size cartel; (2) the schedule of leniency (all reporters can get
leniency or only the first reporter can) does not affect the likelihood of cartel formation.
The organization of the paper is as follows. The theoretical model we used in our
experiment is explained in the next section. Our experimental design and procedures are
explained in section 3, and experimental results are discussed in section 4. Finally,
conclusions are given in section 5.
4
There is a vast number of experimental studies on the prisoners’ dilemma. Whether people are
cooperative or not in the game is not the issue we deal with here. What we focus on in this study is
whether firms which already commit themselves strongly to a cartel activity would really use the
leniency program or not.
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2. Model
In our experiment, we used the following two-person prisoner’s dilemma repeated game
as a baseline game that represents a simple oligopoly market. Table 1 shows the payoff
matrix. The N-person case is analogous to the two-person case.
Table 1 is here
In the prisoner’s dilemma game, each player receives π C when they mutually
cooperate (play Cooperate) and π D when they mutually defect (play Defect). The
player who defects receives π DC when the counterpart cooperates and the counterpart
receives π CD . The condition, π DC > π C > π D > π CD , guarantees that mutual defection is
the only equilibrium (the dominant strategy) in the one-shot game.
Now we introduce the leniency program into the baseline game above by
introducing the antitrust authority (AA). The AA investigates each player to find
evidence of collusion. We assume that the AA monitors each player with probability, p.
When the AA discovers evidence of collusion, both players suffer the full fine, F. If the
leniency program is available to the players, each player can report voluntarily and
independently the collusion information to the AA. If one player reports the
information, the other player suffers the full fine, F, and the player who reported suffers
a reduced fine, R < F. Once the collusion is detected, both players fall under the AA’s
control, and they are not allowed to collude anymore.
In our experiment, all players were forced to mutually collude with each other in the
first stage of the prisoner’s dilemma game. Then they decided voluntarily and
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independently whether they would like to report the collusion information to the AA or
not.
Let us consider the incentive conditions for sustaining the collusion. Although all
players are forced to collude in the first stage (prisoners’ dilemma game) in our settings,
we explain the incentive structure including the case that players can defect in the first
stage. There are two kinds of deviations from mutual cooperation. One is a deviation in
the first stage (not colluding) and the other is a deviation in the second stage (reporting
the collusion information to the AA). We assume that both players employ the following
trigger strategy: each player maintains collusion (first stage and second stage) as long as
the other player does so. However, if one player deviates from the collusion either in the
first stage or in the second stage, the other player will never collude with that player
again. Based on this trigger strategy, we can calculate the expected payoffs for four
possible strategies: (1) colluding and not reporting, (2) colluding and reporting, (3) not
colluding and not reporting, (4) not colluding, and reporting. We can examine what the
incentive conditions are for sustaining the collusion in an ordinary repeated game
analysis. In the following discussion, we examine whether a player has an incentive for
unilateral deviation by comparing expected payoffs of the four cases above under the
condition that his counterpart chooses the strategy of colluding and not reporting.
(1) The expected payoff for the colluding and not reporting strategy ( π CNR )
In this case, a player does not defect in both the first stage and the second stage.
However, if the pair is investigated by the AA with probability p, both players suffer the
full fine F and they can not collude again any more in all the periods thereafter. On the
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other hand, if the pair is not investigated by the AA (the probability= (1 − p) ), they can
continue to collude in the next period, too. Therefore, the expected payoff for this
strategy with the discount factor δ (0 < δ < 1) is as follows.
π CNR = p[(π C − F ) + δ ⋅ π D + δ 2 ⋅ π D + "] + (1 − p) ⋅ [π C + δ ⋅ π CNR ]
δ ⋅π D 

= p (π C − F ) +
+ (1 − p) ⋅ [π C + δ ⋅ π CNR ] .
1 − δ 

Rearranging,
π CNR =
δ ⋅π D 
p
1− p

πC − F +
+
π C . ……………………. (1)


1 − δ + pδ 
1 − δ  1 − δ + pδ
(2) The expected payoff for the colluding and reporting strategy ( π CR )
In this case, a player defects in the second stage. Even if the pair is investigated by
the AA, the defecting player receives a reduced fine, R, while the other player suffers
the full fine, F. The pair can not collude in all the periods thereafter. Therefore, the
expected payoff with the discount factor δ (0 < δ < 1) in this case is as follows.
π CR = (π C − R) + δ ⋅ π D + δ 2 ⋅ π D + " = (π C − R) +
δ ⋅π D
……………… (2)
1−δ
(3) The expected payoff for the not colluding and not reporting strategy ( π NCNR )
In this case, no collusion occurs. Therefore, the expected payoff in this case is as
-8-
follows.
π NCNR = π DC + δ ⋅ π D + δ 2 ⋅ π D + " = π DC +
δ ⋅π D
………………..…… (3)
1−δ
(4) the expected payoff for the not colluding and reporting strategy ( π NCR )
In this case as well, no collusion occurs. Therefore, the expected payoff is the same
as equation (3).
π NCR = π DC + δ ⋅ π D + δ 2 ⋅ π D + " = π DC +
δ ⋅π D
……………………… (4)
1−δ
From the all the calculations above, π CNR ≥ π CR , π NCR , π NCNR are the necessary and
sufficient conditions for each player to sustain the collusion (colluding and not
reporting) if the other player also chooses the same strategy. In our experimental setting,
π CNR equals about 157, π CR equals about 115, π NCNR and π NCR equal about 140.
Since only unilateral deviation from equilibrium is considered according to the Nash
concept, these conditions can be applied to not only the game which consists of two
people but also the game which consists of more than two people. In addition, the
conditions can be applied to the case that the schedule of coverage of reduced fee is
limited to only the first reporting player.
In our experiments, we set the parameters so as to satisfy the condition that
sustaining the collusion is an equilibrium. Therefore, in our experiment, we can expect
subjects to use the colluding and not reporting strategy in both two-person and
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seven-person cases.5 The following is the first null hypothesis to be investigated in our
experiment.
Hypothesis 1: The colluding and not reporting strategy is observed in the
two-person case as frequently as in the seven-person case.
In the previous theoretical literature, only two-person games are considered. Under
the leniency program, however, one may expect that the larger the number of colluding
members, the larger the probability that at least one member of the group deviates from
the collusion, even if such a probability for each member is small. Further, such a
deviation from the collusion could be accelerated if only the first member who reports
the collusion information is given a reduced fine because each player may rush to get a
reduced fine. To pursue such an institutional design issue, we compared different
schedule types of reduced fine. One schedule is that only the first reporter can get a
reduced fine. The other schedule is that all members that report the collusion
information are given a reduced fine. Therefore, the next null hypothesis is as follows.
Hypothesis 2: The rate of collusion is not significantly different between the case
that only the first reporting player is given a reduced fine and the case that all reporting
players are given a reduced fine.
5
These incentive conditions cannot exclude other equilbria. Our game can be reduced to a kind of
stag-hunt game in which both “colluding and reporting” and “colluding and not reporting” are
equilibria. We set payoffs in the first stage prisoner’s dilemma game so that not reporting is a payoffdominant and risk-dominant equilibrium and reporting is not a risk-dominant equilibrium. Therefore,
colluding and not reporting is considered as a plausible equilibrium in our experiment.
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Based on this theoretical model and these behavioral hypotheses, we conducted a
series of experiments. The details of the experiments are explained in the next section.
3. Experiments
Four sessions were conducted at Kyoto Sangyo University in 2004. One session is for
the case with two player groups and three sessions were for the case with seven player
groups. In each session, three treatments were ran sequentially. The first session
consisted of eight periods of prisoners’ dilemma game to make subjects understand that
sustaining collusion is the most profitable outcome (players had to collude). Each
treatment of the following two treatments consisted of five games that include various
numbers of periods (each game was continued with probability of 0.8). Twenty eight
subjects participated in each session (fourteen groups for the session of two-person
groups and twelve groups for the three sessions of seven-person groups). Subjects were
paid individually in cash according to their experimental results. No subject participated
in more than one session. Our experimental subjects were recruited from various majors
at Kyoto Sangyo University.
The experimental procedures were programmed and conducted on z-Tree
(Fischbacher (1999)) with computers with a network connection. Subjects were
randomly assigned to a booth with partitions in front and on both sides of the desk in the
laboratory. It was impossible for them to make direct contact, i.e., by talking, making
eye contact, with other subjects during the session.
The instructor distributed the written instructions to the subjects and read them
aloud to make all the parameters and rules of the experiment common knowledge
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among subjects.6 To make subjects understand the instructions clearly, practice periods
were run before the actual experiment started. 7 Before the actual session started,
subjects practiced clicking their mouses according to the experimenter’s directions to
get used to how to manipulate the computers and how to understand the information
shown on the screen for their decision making. They were not allowed to make any free
decisions until the actual period started. Table 2 summarizes all the treatments.
Table 2 is here
At the beginning of each session, subjects were told that they were going to
experience three kinds of treatments and the result of the first treatment would be paid
for certain but only one of the results of the other two treatments would be paid by
choosing one of them by lottery at the end of all three treatments. The experimenter read
the instructions for each treatment at the beginning of each treatment, so subjects were
not aware of the details of each treatment until just before the treatment began.
Therefore, there was no incentive for subjects to sacrifice their profits in one treatment
in order to make higher profits in a later treatment.8 All subjects were restricted to
colluding in the first stage in the second and third treatments. In the second stage of the
treatments, they decided whether to report the colluding activity to the AA. At the end
of each period, individual decisions of intra-group members were revealed to each
6
The experiment instructions are available upon request.
A practice treatment was run before the second and the third treatments since the first treatment is
not complex at all.
8
However, since subjects could learn how cooperative others are in the second treatment, the result
in the third treatment is not completely independent from the result of the previous treatment in a
rigorous sense. We assume they can be treated as independent data in our analysis.
7
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player, plus whether the collusion activity in their group was found by the AA or not.9
However, the identities of subjects and where they sat were kept confidential to
guarantee anonymity among subjects.
The second treatment was the case that all players who report the information could
get a reduced fine. In this treatment, subjects played with the same group members for
five sessions in sequence.
The third treatment was the case that only the first player who reported the
information could get a reduced fine. As in the second treatment, subjects played with
the same partner (two-person group case) or same group members (seven-person group
case) for five sessions in sequence. Within each session, the number of repetitive
periods was not known beforehand since each session was ended with probability of
δ = 0.8 .
All sessions lasted about two hours. During the experiments, subjects’ earnings were
represented by points. They were told in the instructions that one point would be
exchanged for five yen at the end of the experiment. The average payment for subjects
in the two-person group experiment was 4,972 yen (about 45 US dollars), and the
average payment in the seven-person group experiment was 3,490 yen (about 32 US
dollars) approximately.
4. Results
9
We did not tell subjects that the experiment was about anti-cartel policy. Instead of telling them
that a cartel formation of their group was discovered by the AA, we simply told them that their group
had drawn a payoff reduction lottery. We did not use any terms such as cooperation, defection,
reporting and not reporting, but more neutral terms, such as A or B (in the first stage), choose C or D
(in the second stage).
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To verify the two hypotheses described at the end of section 2, we estimated the
following logistic regression model by using data pooled from the two-person and
seven-person cases.
Pr ob( Dissolve = 1) = F [ β 0 + β1 ⋅ Group + β 2 ⋅ Leniency + β 3 ⋅ Game] ……………(5)
Dissolve is a response variable, which is 1 when at least one group member deviates
from the collusion and 0 otherwise. Group is a dummy variable, which is 1 for the
seven-person case and 0 for the two-person case. Leniency is a dummy variable, which
is 1 when all who report are given reduced fines and 0 when only the first player who
reports is given a reduced fine. Game is the number of games, and F is a logistic
function. The estimated coefficients and other statistical information are shown in Table
3.
Table 3 is here
From Table 3, one can see that the coefficients for Constant, Group are significant
(p<0.10). The coefficient of Group is significantly positive, which indicates that the rate
of cartel dissolution is significantly higher in the seven-person case than in the
two-person case. Hence, Hypothesis 1 is rejected. The coefficient for Leniency is not
significant, which means that the schedule of leniency does not have a strong impact on
people’s behavior in our experimental parameters. Hence, Hypothesis 2 is not rejected.
From this result, we can conclude that limiting the number of firms which can enjoy the
leniency program does not have significant impact on the ability of collusive firms to
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maintain their collusion. The main results of our experiments are summarized below.10
Result 1: The (colluding and) not reporting strategy was observed more frequently
in the two-person case than in the seven-person case.
Result 2: The rate of cartel dissolution was not significantly different between the
case that only the fastest reporter can use the leniency program and the case that all
reporters are allowed to use the program.
Besides these results, one can ask whether or not subject behaviors changed from
game to game. Subjects could have gained enough experience and could have become
familiar with our experimental environment as the games proceeded. The coefficient of
Game is not significant, which means that there was no particular tendency or decay of
collusion across games.
Figure 1 and Figure 2 show the time series data for the number of the groups
sustaining collusion during the sessions in the two-person case session, and Figure 3-8
show the similar graphs for the seven-person case sessions.
Figure 1, 2, 3, 4, 5, 6, 7, 8 are here
5. Conclusions
We studied two kinds of leniency programs through laboratory experiments. It is
10
These results were confirmed by a chai-square test of independence.
- 15 -
expected that the larger the group, the larger the probability of cartel dissolution will be.
In addition, the deviation from collusion could be accelerated if only one firm is given
a reduced fine.
Based on the predictions above, under a simplified oligopoly market, we
experimentally controlled the following two factors to compare several institutional
designs of leniency programs; 1) group size: the number of members in a group, small
group (two members) or large group (seven members), 2) schedule of reduced fine: only
the first reporter of cartel information is given a reduced fine, or all reporters are given
reduced fines.
The experimental results showed that (1) the larger the number of cartel members in
a group is, the weaker their ability to maintain the collusion is, and (2) changing the
schedule of reduced fine does not have a significant impact on firms’ ability to maintain
collusion: limiting the number of firms which can enjoy leniency does not make people
rush to dissolve their collusion by reporting.
We can provide several policy implications from our experimental findings. The
average size of a cartel in the real world consists of about six firms. Therefore the
seven-player case in our experiments nearly corresponds to the real-world situation. We
found that under the two leniency programs, most seven-member groups easily
terminate their collusion. Therefore, we can predict that the leniency program could be
fairly effective for regular size cartel groups in reality.11 However, we did not run
experiments for the situation without the leniency programs. By comparing the current
11
Leniency programs set up in the European Union in 1996 achieved some notable successes in
prosecuting cartels. (see European Union’s Official Journal Legislation (OJL)（98．1.21~03．
12.16）) From data of 31 cartels prosecuted between January 21, 1998 and December 16, 2003 we
can obtain that the average number of firms forming a cartel is about six and by applying leniency
programs the fines for cartel members are reduced by 10% to 100% according to evidence brought
to AA.
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results with the results without the leniency program，we can predict more precisely the
power of leniency programs. In addition, the effect of changing the amount of a fine has
not been investigated in this study. Hence, it is our future task to examine how severe a
penalty is appropriate to prevent cartel formation.
- 17 -
References
Apesteguia, J., M. Dufwenberg and R. Selten (2004): “Blowing the Whistle,” mimeo.
Brisset, K. and L. Thomas (2002): “Leniency Program: A New Tool of the Competition
Policy to Deter Cartel’s Activity,” mimeo.
Fischbacher, U. (1999): “z-Tree: A Toolbox for Readymade Economic Experiments,”
Working Paper No. 21, University of Zurich.
Hinloopen, J. (2002): “The Effectiveness of Leniency Programs under European Style
Antitrust Legislation,” mimeo.
The Japan Fair Trade Commission’s Annual Reports between 1994 and 2004.
Lowe, P. (2003), “What’s the Future for Cartel Enforcement,” presented at the
Conference for Understanding Global Cartel Enforcement at Brussels, February 11.
Monti, M. (2002), “The Fight Against Cartels,” summary of the Talk by Mario Monti
to EMAC, September 11.
Motta, M. and M. Polo (2003): “Leniency Programs and Cartel Prosecution,”
International Journal of Industrial Organization, 21(3), 347-379.
Spagnolo, G. (2000): “Optimal Leniency Program,” mimeo.
- 18 -
Table 1. Two-person prisoner’s dilemma game
Player 2
Cooperate
Defect
Player 1
Cooperate
Defect
πC , πC
π CD , π DC
π DC , π CD
πD, πD
(Note) π DC > π C > π D > π CD .
In our experimental setting, π C = 40, π CD = 10, π DC = 60, π D = 20.
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Table 2. Treatment details
Sessions
Two-person group
Treatment 1
Seven-person group
No leniency programs
Treatment 2 (5 games)
All players can get reduced fines
Treatment 3 (5 games)
Only the first player can get a reduced fine
Total subjects
28
84
The number of groups (each session)
14
4
Fines (F: fine, R: reduced fine)
F=40, R=5
δ = 0 .8
Discount factor
(Note) Discount factor means the probability that each game is continued. Subjects were
told that each period in each game would be continued with probability of 0.8.
- 20 -
Table 3. Logistic regression on cartel dissolution
Dependent variable: Dissolve (if a cartel is dissolved =1, otherwise=0)
Number of observation =260,
Log likelihood =-112.23829
Variable
coefficients
Std. Err.
z
p
Constant
-1.24
0.45
-2.78
0.01
Group (two = 0, seven = 1)
3.41
0.35
9.75
0.00
Leniency (only the first one =
0, all ones = 1)
0.18
0.34
0.51
0.61
Game
-0.15
0.12
-1.20
0.23
(Note) We simply assumed those groups whose cartels were dissolved by lottery could
have maintained their collusion if they did not draw the payment reduction lottery,
which means that the anti-trust agency investigated those firms.
- 21 -
Figure 1. Time series of the number of collusive groups when
all players who report get reduced fines (two-person case)
14
The number of groups
12
10
8
6
4
2
0
1 1 2 3 4 5 6 1 2 3 4 5 1 2 3 4 5 6 7 1 2 3
Period
Figure 2. Time series of the number of collusive groups when
only the first player who reports gets a reduced fine (twoperson case)
14
The number of groups
12
10
8
6
4
2
0
1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 1 1 2 3 1 1 2 3 4
Period
- 22 -
Figure 3. Time series of the number of collusive groups when all players who report get
reduced fines (seven-person case) -session 1
The number of groups
4
3
2
1
0
1 2
3 4
5 6
7 8 9 10 11 12 13 14 15 1 2
3 4 1
1
2 3 4 5
6 7 1 2
3 4
Period
Figure 4. Time series of the number of collusive groups when all players who report get
reduced fines (seven-person case) -session 2
3
groups
The number of collusive
4
2
1
0
1
2
3
4
1
2
3
4
1
2
1
2
1
2
3
4
Period
The number of collusive groups
Figure 5. Time series of the number of collusive groups when all players who report get
reduced fines (seven-person case) -session 3
4
3
2
1
0
1
1
2
1
2
3
4
5
Period
- 23 -
6
7
1
2
3
4
1
Figure 6. Time series of the number of collusive groups when only the first player who
reports gets a reduced fine (seven-person case) - session 1
The number of groups
4
3
2
1
0
1
2
1
2
3
1
2
3
1
2
3
4
5
6
7
8
1
2
3
4
Period
Figure 7. Time series of the number of collusive groups when only the first player who
reports gets a reduced fine (seven-person case) -session 2
3
groups
The number of collusive
4
2
1
0
1
2
3
4
1
2
3
4
1
2
1
2
1
2
3
4
Period
Figure 8. Time series of the number of collusive groups when only the first player who
reports gets a reduced fine (seven-person case) -session 3
3
groups
The number of collusive
4
2
1
0
1 2 3 4 5 6 7 8 9 1 2 3 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 1
Period
- 24 -